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America's Next Top Model -- Part III

Razor's Edge
Top Models.  Let's sexualize kids.
What could possibly go wrong?
Resuming our discussion of modeling from Part I and Part II...

Recall that in his Nobel laureate speech, "The Pretence of Knowledge," Friedrich August von Hayek (the father, we may suppose, of Freddy September) pointed to organized complexity as a major issue in economics and similar fields:

Organized complexity... means that the character of the structures showing it depends not only on the properties of the individual elements of which they are composed, and the relative frequency with which they occur, but also on the manner in which the individual elements are connected with each other. In the explanation of the working of such structures we can for this reason not replace the information about the individual elements by statistical information, but require full information about each element if from our theory we are to derive specific predictions about individual events. Without such specific information about the individual elements we shall be confined to what on another occasion I have called mere pattern predictions - predictions of some of the general attributes of the structures that will form themselves, but not containing specific statements about the individual elements of which the structures will be made up. [Emph. added]

In classical thought, the part that depends on "the properties of the individual elements of which they are composed" is the material cause, a/k/a "reductionism." (The term 'matter' means simply the elements of which a thing is composed. Bricks are the matter of a wall.)

The part that depends on "the manner in which the individual elements are connected with each other" is the formal cause. In modern parlance this is sometimes called "emergent properties" because the whole system has the property while the individual elements do not.

In other words, it's the form (pattern, organization) that is the key to intelligibility. Given a set of interconnected elements X1, X2,... Xn, we cannot legitimately replace the specific Xs with X-bar as we may in cases of disorganized complexity. At best we would obtain only statistical conclusions about the entire system -- as we do in fact regarding quantum mechanics.

When there are only a few elements in the system, the scientist introduces simplifications: infinite Euclidean space, ideal gasses, perfectly elastic collisions, and the like. Arrhenius' law relating CO2 to temperature assumes the atmosphere extends to infinity. TOF read a joke - he has forgotten where - about using models to predict the SuperBowl, which is a sort of football game sometimes (but not this past year) played by two teams. In the punchline, the physicist says, "consider each player to be a perfectly elastic sphere on an infinite Euclidean field..." Mathematics tends to become ornery when bumping up against boundary values* and it is precisely at the extremes where many models pop their suspenders.
(*) boundary values. TOF has his old college text, Fourier Series and Boundary Value Problems, by Ruel Churchill, which he will someday nerve himself to re-read.

Comments

( 1 comment — Leave a comment )
whswhs
Mar. 29th, 2014 02:07 pm (UTC)
That textbook title sounds awfully familiar. I'm pretty sure we used Churchill in my applied math course series at UC San Diego, back in 1970-1971.
( 1 comment — Leave a comment )

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